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A133161
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Indices of the triangular numbers which are also centered triangular number.
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2
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1, 4, 16, 61, 229, 856, 3196, 11929, 44521, 166156, 620104, 2314261, 8636941, 32233504, 120297076, 448954801, 1675522129, 6253133716, 23337012736, 87094917229, 325042656181, 1213075707496, 4527260173804, 16895964987721
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OFFSET
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1,2
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COMMENTS
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Also, indices of the triangular numbers which are sums of three consecutive triangular numbers (see A129803).
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LINKS
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Table of n, a(n) for n=1..24.
A. Kozikowska, Topological classes of statically determinate beams with arbitrary number of supports, JOURNAL OF THEORETICAL AND APPLIED MECHANICS 49, 4, pp. 1079-1100, Warsaw 2011; (see Eq. 5.18). - N. J. A. Sloane, Dec 17 2011.
Index entries for linear recurrences with constant coefficients, signature (5,-5,1).
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FORMULA
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a(n+2)=4*a(n+1)-a(n)+1.
a(n+1)=2*a(n)+0.5+0.5*(12*a(n)^2+12*a(n)-15)^0.5.
G.f.: x*(1-x+x^2)/(1-x)/(1-4*x+x^2). - R. J. Mathar, Oct 24 2007
a(n)=-(1/2)-(1/4)*sqrt(3)*[2-sqrt(3)]^n+(1/4)*sqrt(3)*[2+sqrt(3)]^n+(3/4)*[2-sqrt(3)]^n+(3/4) *[2+sqrt(3)]^n, with n>=0 - Paolo P. Lava, Jul 30 2008
a(n)-a(n-1)= A005320(n-1). - R. J. Mathar, Mar 14 2016
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MATHEMATICA
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LinearRecurrence[{5, -5, 1}, {1, 4, 16}, 30] (* Harvey P. Dale, Aug 29 2017 *)
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CROSSREFS
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Cf. A001834, A102871, A128862, A129803, A001571.
Sequence in context: A126929 A338531 A268452 * A103820 A206570 A206790
Adjacent sequences: A133158 A133159 A133160 * A133162 A133163 A133164
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KEYWORD
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nonn,easy
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AUTHOR
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Richard Choulet, Oct 09 2007
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STATUS
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approved
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